Monday 9th of December 2024, 13:30-14:30 in HG03.054
Malte Leimbach
Noncommutative geometry, quantum metric spaces and spectral truncations
Spectral geometry is about infering geometric information (about a compact Riemannian manifold, say) from the spectrum of canonically associated differential operators. This principle is very attractive for noncommutative geometry, where there are no points, but one rather works dually with appropriate generalizations of *-algebras of functions. In practice, only limited spectral data is available, however, so one is bound to work with certain "fuzzy" approximations of (noncommutative) geometric objects. In this talk we will go on a brief tour through "noncommutative topological spaces", "quantum metric spaces" and "spectral truncations". If time permits we will take a glimpse at compact quantum groups (which generalize both compact groups and "duals" of discrete groups) and see how to view them as compact quantum metric spaces.